To find the average rate of change of a function over a given interval, we use the formula:

$\text{Average Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}$

In this case, the given interval is $-1 \leq x \leq 5$.

From the table, we can extract the values for $x$ and $y$:

• When $x = -1$, $y = 3$
• When $x = 5$, $y = -5$

Using the formula:

$\text{Average Rate of Change} = \frac{-5 - 3}{5 - (-1)} = \frac{-8}{6} = -\frac{4}{3}$

Thus, the average rate of change over the interval $-1 \leq x \leq 5$ is $-\frac{4}{3}$.

Would you like a more detailed explanation or have any further questions?

Here are five related questions you could explore:

1. How does the average rate of change differ from the instantaneous rate of change?
2. Can the average rate of change over different intervals of this table be positive?
3. What is the significance of the average rate of change being negative in this context?
4. How can you interpret the rate of change geometrically on a graph?
5. How would you compute the average rate of change for non-linear functions?

Tip: When working with tables, always check the points carefully before applying the rate of change formula.